Another bridge between Nim and Wythoff

Eric Duchene (1, 2) , Aviezri S. Fraenkel (3) , Sylvain Gravier (4) , Richard J. Nowakowski (5)

1 Leibniz - IMAG - Laboratoire Leibniz
2 LIESP - Laboratoire d'Informatique pour l'Entreprise et les Systèmes de Production
3 Dept. of Computer Science and Applied Mathematics
4 IF - Institut Fourier
5 Department of Mathematics and Statistics [Canada]

The P positions of both two-heap Nim and Wythoff's games are easy to describe, more so in the former than in the latter. Calculating the actual G values is easy for Nim but seemingly hard for Wythoff's game. We consider what happens when the rules for removing from both heaps are modified in various ways.

Keywords: combinatorial games; graph theory

Domains: Discrete Mathematics [cs.DM]

Eric Duchene, Aviezri S. Fraenkel, Sylvain Gravier, Richard J. Nowakowski. Another bridge between Nim and Wythoff. The Australasian Journal of Combinatorics, 2009, 44, pp.43-56. ⟨hal-00408010⟩